When \(q\ge 0\) , for any “sufficiently uniform” (e.g. dyadic) partition of \(K\) , one may always define the \(L^q\) -spectrum of any finite measure with respect to such a partition (see, for example, [1]}).
When \(q<0\) , such an operation is more delicate since the intervals in a partition can intersect \(K\)  on sets of disproportionately small \(\mu \) -measure.
p:lq-lim essentially states that the partitions \(\lbrace \pi (\eta ):\eta \in \mathcal {F}(t)\rbrace \)  of \(K\)  for \(t>0\)  avoid this issue.
